波兰空间分割原理和Halpern-Läuchli定理
Polish space partition principles and the Halpern-Läuchli theorem
摘要：
Halpern-Läuchli定理，一个关于树的组合结果，由于Harrington使用强迫的想法，承认了一个优雅的证明。在试图提取这个证明的组合本质，我们隔离各种划分原则的产品完美波兰空间。这些原理直接证明了哈尔彭-劳克利定理，而哈林顿的证明同样可以证明它们的一致性。我们还表明，这些原则不ZFC定理表明，他们把下界的连续的大小。
英文摘要：
The Halpern-Läuchli theorem, a combinatorial result about trees, admits an elegant proof due to Harrington using ideas from forcing. In an attempt to distill the combinatorial essence of this proof, we isolate various partition principles about products of perfect Polish spaces. These principles yield straightforward proofs of the Halpern-Läuchli theorem, and the same forcing from Harrington's proof can force their consistency. We also show that these principles are not ZFC theorems by showing that they put lower bounds on the size of the continuum.
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